Alternatives for flow solution at the leading edge of gravity currents using the shallow water equations

ABSTRACT

The shallow water equations (SWEs) are implemented in gravity current (GC) models because of the good balance between accuracy and computational effort. In this context appropriate treatment is required at the GC leading edge that is analogous to a moving boundary condition. To date, solution strategies used at the leading edge have not been systematically compared to determine the best alternatives. This work aims to analyse three strategies, comparing results with experiments and Reynolds-averaged Navier–Stokes (NS) models. Two of these alternatives are implemented using method of characteristics theory, while the third alternative, proposed by the authors, constitutes a newer conservative shock-tracking approach. Despite some of the differences in continuity error and computational effort, these solution strategies accurately predicted front trajectories albeit with much less computational effort when compared with NS models. As anticipated, GC shapes yielded by one-layer SWE models do not compare well particularly at earlier flow stages.

Keywords:

• Boundary conditions
• characteristic equations
• gravity currents
• numerical methods
• shallow water equations